Method for calibrating a specimen stage of a metrology system and metrology system comprising a specimen stage

Abstract

A method for calibrating a specimen stage of a metrology system is provided, in which a specimen that has multiple marks is positioned successively in different calibration positions, each mark is positioned in the photography range of an optical system by means of the specimen stage in each calibration position of the specimen, and the mark position is measured using the optical system. A model is set up that describes positioning errors of the specimen stage using a system of functions having calibration parameters to be determined. The model takes into consideration at least one systematic measurement error that occurs during the measurement of the mark positions. The values of the calibration parameters are determined based on the model with consideration of the measured mark positions.

What is claimed is: 
     
       1. A method for calibrating a specimen stage of a metrology system, the method comprising:
 positioning a specimen having multiple marks successively in a plurality of calibration positions; 
 positioning each mark, by using the specimen stage, within a photography range of an optical system in each calibration position of the specimen, and measuring, using the optical system, the position of the mark; 
 establishing a model in which the positioning error of the specimen stage is represented by a system of functions having calibration parameters to be determined, 
 determining by an additional measurement at least one measurement error that occurs in the measurement of the positions of the marks; 
 representing the at least one measurement error by an additional calibration parameter; and 
 determining the values of the calibration parameters based on the model with consideration of the measured positions of the marks, wherein the model takes into account the at least one measurement error that occurs in the measurement of the positions of the marks. 
 
     
     
       2. The method of  claim 1  in which the at least one measurement error is taken into account linearly in the model. 
     
     
       3. The method of  claim 1  in which determining the values of the calibration parameters comprises using a Gaussian method of least squares of the errors to determine the values of the calibration parameters. 
     
     
       4. The method of  claim 1  in which positioning the specimen comprises positioning the specimen in at least three different calibration positions. 
     
     
       5. The method of  claim 1  in which the at least one measurement error comprises an imaging error of the optical system. 
     
     
       6. The method of  claim 1  in which the at least one measurement error comprises a projection error in the measurement of the mark position due to a tilt of the specimen. 
     
     
       7. The method of  claim 6 , comprising measuring a component of the mark position perpendicular to a plane of the specimen stage in each calibration position. 
     
     
       8. The method of  claim 1  in which the at least one measurement error comprises an error caused by an uneven arrangement of the marks. 
     
     
       9. The method of  claim 1 , comprising moving the specimen stage in a plane to position the marks, in which the at least one measurement error comprises a measurement error that is proportional to the position of the specimen stage perpendicular to the plane. 
     
     
       10. The method of  claim 1 , comprising positioning the specimen stage in an xy-plane, and the at least one measurement error comprises an error that is caused by a rotation of the specimen stage dependent on the x- or y-position of the specimen stage. 
     
     
       11. The method of  claim 1  in which the at least one measurement error comprises an error caused by a gravity-induced deformation of the specimen. 
     
     
       12. The method of  claim 1  in which the at least one measurement error comprises an error caused by the marks being spaced apart by more than a threshold. 
     
     
       13. The method of  claim 1  in which the marks are arranged on the specimen in a Cartesian grid. 
     
     
       14. The method of  claim 13  in which at least one calibration position comprises a rotation of the specimen that is not symmetrical with the grid. 
     
     
       15. The method of  claim 14 , comprising positioning the specimen stage in an xy-plane, and the measurement error comprises an error that depends on the x or y coordinate. 
     
     
       16. The method of  claim 1  in which the system of functions is linear with respect to the calibration parameters. 
     
     
       17. The method of  claim 1 , comprising performing a two-dimensional calibration. 
     
     
       18. The method of  claim 1  in which the specimen is positioned each time on the specimen stage in its calibration positions. 
     
     
       19. The method of  claim 1 , comprising positioning multiple specimens, each having multiple marks, successively in different calibration positions, and positioning each mark on each sample, by using the specimen stage, in each calibration position in the photography range of the optical system, and measuring the mark position using the optical system. 
     
     
       20. The method of  claim 1  in which the model takes into account another measurement error that occurs in the measurement of the positions of the marks when the specimen stage is accurately positioned. 
     
     
       21. A metrology system comprising:
 a specimen stage; 
 a measuring module configured to determine at least one measurement error; and 
 a control unit that controls the specimen stage to bring the specimen stage into a predetermined position, the control unit controlling the specimen stage based on a calibration model that takes into consideration positioning errors of the specimen stage and the at least one measurement error determined by the measuring module that occurs in the calibration of the specimen stage, to bring the specimen stage to the predetermined position, wherein the calibration model representing the at least one measurement error by an additional calibration parameter. 
 
     
     
       22. The metrology system of  claim 21  in which the at least one systematic measurement error comprises an error in the measurement of positions of marks on a specimen that is positioned using the specimen stage. 
     
     
       23. The metrology system of  claim 22  in which the at least one systematic measurement error comprises at least one of (a) an imaging error of an optical system that is used to measure the positions of the marks on the specimen, (b) an error due to a tilt of the specimen, (c) an error caused by an uneven arrangement of the marks, or (d) an error caused by a gravity-induced deformation of the specimen. 
     
     
       24. The metrology system of  claim 21  in which the model comprises a linear function of the at least one systematic measurement error. 
     
     
       25. The metrology system of  claim 24  in which the model comprises a system of functions that represents the positioning error of the specimen stage, the system of functions having calibration parameters to be determined. 
     
     
       26. An apparatus comprising:
 a specimen stage to position a specimen having multiple marks successively in a plurality of calibration positions; 
 an optical system; 
 a control unit to control the specimen stage for positioning each mark within a photography range of the optical system in each calibration position, and control the optical system to measure the position of the mark; 
 a measuring module configured to determine at least one measurement error; and 
 a processing module to establish a model in which the positioning error of the specimen stage is represented by a system of functions having calibration parameters, the model taking into account at least one measurement error that occurs in the measurement of the positions of the marks as determined by the measuring module, the processing module determining the values of the calibration parameters based on the model with reference to the measured mark positions and an additional calibration parameter based on the at least one measurement error. 
 
     
     
       27. The apparatus of  claim 26  in which the at least one measurement error comprises at least one of (a) an imaging error of an optical system that is used to measure the positions of the marks on the specimen, (b) an error due to a tilt of the specimen, (c) an error caused by an uneven arrangement of the marks, or (d) an error caused by a gravity-induced deformation of the specimen. 
     
     
       28. The apparatus of  claim 26  in which the model comprises a linear function of the at least one measurement error.